Question

Calculate the producers' surplus for the supply equation at the indicated unit price
p.
(Round your answer to the nearest cent.)
p = 7 + 2q^1/3; p = 18

Answer 1

producer surplus = area above curve and below given price

\[= PQ - \int\limits_0^Q (7+2q^{1/3}) dq\]
P = 18
Q = 1331/8

Answer 2

after integrating
\[\rightarrow (18)(\frac{1331}{8}) - (7q +\frac{3}{2}q^{4/3}) |_0^{1331/8}\]
\[= \frac{9}{4}(1331)- \frac{7}{8}(1331)-(\frac{3}{16})(\frac{11}{2})(1331)\]
\[= \frac{11}{32}(1331)\]
= 457.53